Geometric characterization of interpolation in the space of Fourier–Laplace transforms of ultradistributions of Roumieu type

• Autores: Piotr Zioło
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 2, 2011, págs. 161-172
• Idioma: inglés
• DOI: 10.1007/s13348-010-0022-8
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We give a geometric characterization of interpolating varieties for the algebra of Fourier–Laplace transforms of ultradistributions of Roumieu type with compact support on the real line in the non-quasianalytic case. In particular, such a characterization is found in the case of classical Gevrey classes. We also provide a relation between interpolating varieties in this case and in the case of Hörmander algebras related to ultradistributions of Beurling type.

• Referencias bibliográficas
  • Albanese A.A., Jornet D., Oliaro A.: Quasianalytic wave front sets for solutions of linear PDO. Integral Equ. Oper. Theory 66, 153–181 (2010)
  • Berenstein C.A., Gay R.: Complex Variables, An Introduction. Graduate Texts in Mathematics, vol. 125. Springer, New York (1991)
  • Berenstein C.A., Gay R.: Complex Analysis and Special Topics in Harmonic Analysis. Springer, Berlin (1995)
  • Berenstein C.A., Li B.Q.: Interpolating varieties for spaces of meromorphic functions. J. Geom. Anal. 5, 1–48 (1995)
  • Berenstein C.A., Li B.Q., Vidras A.: Geometric characterization of interpolating varieties for the (FN)-space {A_{p{}_{\vphantom{0_{0}}}}^0}...
  • Bonet J., Meise R.: Ultradistributions of Roumieu type and projective descriptions. J. Math. Anal. Appl. 255, 122–136 (2001)
  • Bonet J., Domański P.: The structure of spaces of quasianalytic functions of Roumieu type. Arch. Math. (Basel) 89, 430–441 (2007)
  • Bonet J., Meise R., Melikhov S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math....
  • Bonet J., Meise R.: Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear...
  • Bonet, J., Meise, R.: Convolution operators on quasianalytic classes of Roumieu type, Functional analysis and complex analysis, pp. 23–45....
  • Braun R.W., Meise R.: Generalized Fourier expansions for zero-solutions of surjective convolution operators on {{\fancyscript{D}}_{\{\omega\}}(R)'}....
  • Braun R.W., Meise R., Taylor B.A.: Ultradifferentiable functions and Fourier analysis. Results Math. 17, 206–237 (1990)
  • Braun R.W., Meise R., Vogt D.: Existence of fundamental solutions and surjectivity of convolution operators on classes of ultra-differentiable...
  • Braun R.W., Meise R., Vogt D.: Characterization of the linear partial differential operators with constant coefficients which are surjectiv...
  • Franken U., Meise R.: Generalized Fourier expansions for zero-solutions of surjective convolution operators on {{\fancyscript{D}}(R)} and...
  • Komatsu H.: Ultradistributions I, structure theorem and a characterization. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20, 25–105 (1973)
  • Langenbruch M.: Continuous linear right inverses for convolution operators in spaces of real analytic functions. Studia Math. 110, 65–82 (1994)
  • Massaneda X., Ortega-Cerdá J., Ounaïes M.: A geometric characterization of interpolation in {\hat{\fancyscript{E}}'(R)}. Trans. Am. Math....
  • Meise R.: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals. J. Reine Angew. Math. 363, 59–95 (1985)
  • Meise R.: Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type. Studia...
  • Meise R., Taylor B.A.: Sequence space representations for (FN)-algebras of entire functions modulo closed ideals. Studia Math. 85, 203–227...
  • Meise R., Taylor B.A., Vogt D.: Continuous linear right inverses for partial differential operators on non-quasianalytic classes and on ultradistributions....
  • Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press, Oxford University...
  • Meyer T.: Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type. Studia Math. 125, 101–129 (1997)
  • Ounaïes M.: Interpolation by entire functions with growth conditions. Michigan Math. J. 56, 155–171 (2008)
  • Rodino L.: Linear Partial Differential Operators in Gevrey Spaces. World Scientific Publishing Co., Inc., River Edge (1993)
  • Rösner Th.: Surjektivität partieller Differentialoperatoren auf quasianalytischen Roumieu-Klassen. Dissertation, Düsseldorf (1997)
  • Squires W.A.: Necessary conditions for universal interpolation in {\hat{\fancyscript{E}}'}. Can. J. Math. 33, 1356–1364 (1981)
  • Squires W.A.: Geometric condition for universal interpolation in {\hat{\fancyscript{E}}'}. Trans. Am. Math. Soc. 280, 401–413 (1983)